The textbook description of an inductor often involves a coil of wire. Of course, any material other than a perfect ideal insulator has theoretical inductance. All the windings do is multiply the effect by creating overlapping fields. It’s good to keep in mind that inductance is measurable in many non-coils, such as power transmission lines, coax, UTP Ethernet cable and traces on a circuit board.

That brings us to the concept of the load coil. Oliver Heaviside was a British theoretician and practical electrician who reworked Maxwell’s wo equations of electromagnetism, optics and electric circuits into a far simpler set of four vector equations that we use today:

∇ · εE = ρ
∇ × E = −μ∂H/∂t
∇ · μH = 0
∇ × H = kE + ε∂E/∂t,

where ε is permittivity, μ is magnetic permeability, ρ is charge density, and k is the conductivity of the medium. But Heaviside’s brother Arthur had a hand in the idea of a load coil. Arthur was an engineer working for the British Post Office, which at that time had jurisdiction over the nation-wide telephone system. He found that adding more telephones in parallel improved the clarity of the transmitted voices. Oliver showed his brother that current leakage through the multiple phones reduced distortion. This insight led to the introduction of inductive loading coils, which improve telephone line efficiency and are used today in large land-line switching facilities.

Heaviside represented the line as a network of infinitesimally small circuit elements. He discovered what is known as the Heaviside condition, the condition that must be fulfilled for a transmission line to be free from distortion. The Heaviside condition is that the series impedance, Z, must be proportional to the shunt admittance, Y, at all frequencies. In terms of the primary line coefficients the condition is R/G=L/C where R is the series resistance of the line per unit length, L is the series self-inductance of the line per unit length, G is the shunt leakage conductance of the line insulator per unit length, and C is the shunt capacitance between the line conductors per unit length.

From the telephony application, the term loading coil has come to mean an inductance that is specifically designed to cancel shunt capacitance. A typical loading coil for telephony is an 88 mH torrid spaced about every 6,000 ft on a phone line and was used only on subscriber loops at least 18,000 ft long. However, use of digital transmission such as DSL or ASDL made ordinary load coils impractical. The problem was that digital transmission used high frequencies that load coils filtered out. One solution was to re-design the load coil to function as a notch filter tuned to the dead space between the voice band and the ADSL band–high ADSL frequencies are unaltered.

The other application for loading coils is in antennas. Monopole and dipole antennas are designed to act as resonators at a specific frequency. To resonate, the antenna must have a physical length of one quarter of the wavelength of the RF used (or a multiple of that length, with odd multiples usually preferred). At resonance, the antenna acts electrically as a pure resistance, absorbing all the power from the transmitter.

Sometimes the antenna must be shorter than the quarter-wavelength resonant length. Such an electrically short antenna presents capacitive reactance to the transmission line. Some of the applied power reflects back into the transmission line and travels back toward the transmitter. The two currents at the same frequency cause standing waves on the transmission line.

The insertion of a loading coil in series makes an electrically short antenna resonant. The coil has an inductive reactance equal and opposite to the capacitive reactance of the short antenna. Thus the two reactances cancel. The loading coil often sits at the base of the antenna, but it is sometimes inserted in the center of the antenna element (center loading) for more efficient radiation. A point to note, though, is that an inductor also adds electrical resistance to the antenna, reducing radiation efficiency compared to full-size antennas.

The radiation resistance of short antennas can be as low a few ohms in the LF or VLF bands. Resistance in the coil winding is typically comparable to or exceeds the radiation resistance, so loading coils for extremely electrically short antennas must have extremely low impedance at the operating frequency. To reduce skin effect losses, the coil may be made of tubing or Litz wire, with single layer windings, with turns spaced apart to reduce proximity effect resistance.

An additional point is that the capacitive antennas used at low frequencies have extremely narrow bandwidths, so it may be helpful to make the loading coil adjustable to tune the antenna to resonance with the new transmitter frequency. Variometers are often used. Variometers have two coils wired in series such that when a shaft rotates, the inductance goes from being additive to being subtractive. If the coils are in phase, the inductances add. Conversely, coils out of phase are subtractive.

Of course, there are several ways of measuring load coils. Perhaps the most straightforward is to wire the coil in series with a variable resistor, then feed a sine wave at the frequency of interest, f, through the circuit while monitoring inductor voltage with an oscilloscope. Varying the resistance so half the signal generator output voltage is across the inductor gives the point at which inductor impedance equals the value of the variable resistor, R. The inductance L can then be computed from L=R√3/(2πf)

The above technique may be preferable to use of a simple LCR meter because ordinary LCR meters generally test components at one frequency. And the test frequency may not be close to the frequency at which the load inductor will be used. (Pricier models may allow tests of inductance at a selectable frequency.)

It’s also possible to calculate load coil inductance using a voltage-current slope on a scope display. This method uses a pulse generator and a sense resistor. The pulse output is set to a 50% duty cycle or less. Read the peak current and the amount of time between voltage pulses on the scope display. Then the equation L = V×T_on/I_pk gives inductance where T_on is the pulse on time, I_pk is the peak current through the inductor, and V is the top voltage of the pulses.